All the cats in the domestic cat branch of felid tree have slit shaped eyes. Domestic cats, wildcats, sand cats, black footed cats, and jungle cats all share this trait. They are all small cat species.

Pallas cats belong to the leopard cat branch, and share similar eyes with the larger cats despite their other physical characteristics. It is interesting that they've kept the round eyes, because small cats tend to hunt via stealth during low light periods such as dawn/dusk where slit shaped eyes are an advantage.

This is a trait a nearly universal eye shape in small cat species. Even those in the leopard cat branch (rusty spotted cat, flat headed cat) and other branches related to other large cats (pampas cat in the ocelot branch, marbled cat in the bay cat branch, bobcats in the lynx branch, serval in the caracal branch, etc).

Depends on the light.

Here's Emily in full daylight:

And here she is in low light conditions: